For what it is worth, it's usually less expensive to rent a car from a location not near the airport

Need more info from you to be of help. Where are you planning to drive once you leave DFW? Are you planning a one-way rental or will you be returning future of space travel to DFW? Are you willing to take alternate transportation to car rental site to pick up your vehicle? Also, how long will you be renting the car? If only for a short period, the transportation costs to get you to/from DFW Airport future of space travel might off-set and rental cost savings?
For what it is worth, it's usually less expensive to rent a car from a location not near the airport. Have you check rental rates from your preferred car rental company when picking up from rental locations in Fort Worth, Dallas, Arlington, Hurst, Euless, Bedford, Grapevine or any of the other town and suburbs around the Dallas/Fort Worth Metroplex???
Because of construction on the North side of the airport, the local car rental companies in that direction, such as in Grapevine, are far less accessible. A cab to these locations will be in the $40-$50 range.
The downside of using these locations is the limited service hours the provide. Basically they are 9-6 operations, six days a week. OTOH, Hertz and Avis allow you to return to the airport with no additional charges.
Thanks, Jeff801, for the details about off-airport options. Our flight is scheduled to arrive at 2:30 p.m. on 11/23--the Friday after Thanksgiving. We will spend the first two nights in Dallas. Would it be better to pick up the car in Grand Prairie/North Arlington or in downtown Dallas near where we will be staying? We are used to big city driving.
Driving in downtown Dallas is not markedly different from other big cities, but neither is the parking any cheaper. The difference in cab fare from DFW to Grand Prairie or Arlington, compared to that to downtown Dallas would be eaten up by the parking fees. (I can't speak to cab fare within the city, I have never used any.) My guess would be that you would be better off picking up the car in the city on the day after you arrive. If your plane is on time, and you check bags, you are unlikely to get to your destination earlier than 4:30-5:00. If you select a nearby place for dinner, you won't need a car until the following morning at the earliest.